3 problems

Caucci's conjecture. If

Let $X$ be a smooth projective variety and let $L$ be a line bundle on $X$. For every proper subvariety $Z\varsubsetneq X$, write $(L^{\dim Z}.Z)$ for the intersection number of…

Basepoint free conjecture. The linear system $|b(K_X+S+A)|$ is basepoint free for every $b\gg 0$.